Belief Data Analyses
26 November, 2023
## [1] "Folder already exists"## [1] "Folder already exists"## [1] "Folder already exists"Responder Trials
| Total | Participants Excluded (Sample A) | Participants Included (Sample A) | Observations Lost (< 90% Valid Gaze Samples) | Observations Lost (NA for CorrectIncorrect) | NA Rows for FileName | NA Rows for rRTsacc | Trials with Incorrect Response | Observations Lost (NA for PredictiveGazeFace | Observations Lost with SRT <0.15s & > 3s) |
|---|---|---|---|---|---|---|---|---|---|
| 86 | 22 | 64 | 553 | 0 | 0 | 1048 | 92 | 0 | 1442 |
| Belief | Mean (%) | SD (%) | Mean (%) | SD (%) | Mean (%) | SD (%) | Mean (%) | SD (%) |
|---|---|---|---|---|---|---|---|---|
| AI | 81.99588 | 21.18553 | 81.99588 | 21.18553 | 63.78601 | 20.35482 | 7.690329 | 15.852073 |
| Human | 82.20721 | 16.19655 | 82.20721 | 16.19655 | 67.39865 | 17.01739 | 5.048799 | 9.181748 |
Accuracy
Plot
Generalised Linear Mixed Effect Model for Responder Accuracy
| Estimate | Std. Error | z value | Pr(>|z|) | |
|---|---|---|---|---|
| (Intercept) | 7.669 | 0.723 | 10.608 | 0.000 |
| CongruencyIncongruent | -4.630 | 0.718 | -6.453 | 0.000 |
| BeliefHuman | 1.527 | 0.665 | 2.295 | 0.022 |
| AvatarRobot | 1.973 | 0.589 | 3.349 | 0.001 |
| CongruencyIncongruent:BeliefHuman | -0.847 | 0.721 | -1.175 | 0.240 |
| CongruencyIncongruent:AvatarRobot | -1.485 | 0.778 | -1.908 | 0.056 |
| BeliefHuman:AvatarRobot | -1.380 | 0.927 | -1.489 | 0.137 |
| CongruencyIncongruent:BeliefHuman:AvatarRobot | 1.042 | 1.205 | 0.865 | 0.387 |
## (Intercept)
## 7.6693093
## CongruencyIncongruent
## -4.6304260
## BeliefHuman
## 1.5266551
## AvatarRobot
## 1.9732340
## CongruencyIncongruent:BeliefHuman
## -0.8467675
## CongruencyIncongruent:AvatarRobot
## -1.4850553
## BeliefHuman:AvatarRobot
## -1.3801848
## CongruencyIncongruent:BeliefHuman:AvatarRobot
## 1.0416062## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: CorrectIncorrect ~ Congruency + Belief + Avatar + Congruency:Belief +
## Congruency:Avatar + Belief:Avatar + Congruency:Belief:Avatar +
## (1 | SubjectID) + (1 | TrialID)
## Data: UseableData
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
##
## AIC BIC logLik deviance df.resid
## 691.4 760.4 -335.7 671.4 7317
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -28.5913 0.0131 0.0344 0.0630 1.4709
##
## Random effects:
## Groups Name Variance Std.Dev.
## TrialID (Intercept) 8.194 2.862
## SubjectID (Intercept) 2.390 1.546
## Number of obs: 7327, groups: TrialID, 72; SubjectID, 64
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) 7.6693 0.7229 10.608
## CongruencyIncongruent -4.6304 0.7176 -6.453
## BeliefHuman 1.5267 0.6654 2.295
## AvatarRobot 1.9732 0.5892 3.349
## CongruencyIncongruent:BeliefHuman -0.8468 0.7205 -1.175
## CongruencyIncongruent:AvatarRobot -1.4851 0.7784 -1.908
## BeliefHuman:AvatarRobot -1.3802 0.9270 -1.489
## CongruencyIncongruent:BeliefHuman:AvatarRobot 1.0416 1.2045 0.865
## Pr(>|z|)
## (Intercept) < 2e-16 ***
## CongruencyIncongruent 1.1e-10 ***
## BeliefHuman 0.021762 *
## AvatarRobot 0.000811 ***
## CongruencyIncongruent:BeliefHuman 0.239896
## CongruencyIncongruent:AvatarRobot 0.056410 .
## BeliefHuman:AvatarRobot 0.136509
## CongruencyIncongruent:BeliefHuman:AvatarRobot 0.387176
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) CngrnI BlfHmn AvtrRb CnI:BH CnI:AR BlH:AR
## CngrncyIncn -0.538
## BeliefHuman -0.360 0.116
## AvatarRobot -0.079 0.108 0.135
## CngrncyI:BH 0.151 -0.420 -0.478 -0.139
## CngrncyI:AR 0.118 -0.387 -0.096 -0.745 0.332
## BlfHmn:AvtR 0.051 -0.067 -0.368 -0.635 0.344 0.473
## CngrI:BH:AR -0.076 0.220 0.267 0.480 -0.586 -0.642 -0.763## We fitted a logistic mixed model (estimated using ML and BOBYQA optimizer) to
## predict CorrectIncorrect with Congruency, Belief and Avatar (formula:
## CorrectIncorrect ~ Congruency + Belief + Avatar + Congruency:Belief +
## Congruency:Avatar + Belief:Avatar + Congruency:Belief:Avatar). The model
## included SubjectID as random effects (formula: list(~1 | SubjectID, ~1 |
## TrialID)). The model's total explanatory power is substantial (conditional R2 =
## 0.84) and the part related to the fixed effects alone (marginal R2) is of 0.32.
## The model's intercept, corresponding to Congruency = Congruent, Belief = AI and
## Avatar = Anthropomorphic, is at 7.67 (95% CI [6.25, 9.09], p < .001). Within
## this model:
##
## - The effect of Congruency [Incongruent] is statistically significant and
## negative (beta = -4.63, 95% CI [-6.04, -3.22], p < .001; Std. beta = -4.63, 95%
## CI [-6.04, -3.22])
## - The effect of Belief [Human] is statistically significant and positive (beta
## = 1.53, 95% CI [0.22, 2.83], p = 0.022; Std. beta = 1.53, 95% CI [0.22, 2.83])
## - The effect of Avatar [Robot] is statistically significant and positive (beta
## = 1.97, 95% CI [0.82, 3.13], p < .001; Std. beta = 1.97, 95% CI [0.82, 3.13])
## - The effect of Congruency [Incongruent] × Belief [Human] is statistically
## non-significant and negative (beta = -0.85, 95% CI [-2.26, 0.57], p = 0.240;
## Std. beta = -0.85, 95% CI [-2.26, 0.57])
## - The effect of Congruency [Incongruent] × Avatar [Robot] is statistically
## non-significant and negative (beta = -1.49, 95% CI [-3.01, 0.04], p = 0.056;
## Std. beta = -1.49, 95% CI [-3.01, 0.04])
## - The effect of Belief [Human] × Avatar [Robot] is statistically
## non-significant and negative (beta = -1.38, 95% CI [-3.20, 0.44], p = 0.137;
## Std. beta = -1.38, 95% CI [-3.20, 0.44])
## - The effect of (Congruency [Incongruent] × Belief [Human]) × Avatar [Robot] is
## statistically non-significant and positive (beta = 1.04, 95% CI [-1.32, 3.40],
## p = 0.387; Std. beta = 1.04, 95% CI [-1.32, 3.40])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald z-distribution approximation.## The model included SubjectID as random effects (formula: list(~1 | SubjectID, ~1 | TrialID))## [1] "very strong evidence against"
## (Rules: jeffreys1961)## [1] 0.01689006## [1] 0.01689006## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUEIndependent Samples t-Test (Accuracy by Belief)
The mean Accuracy in the AI group was 97.486 (SD = 5.559), whereas the mean in the Human group was 98.842 (SD = 2.933). A Welch two-samples t-test showed that the difference was statistically significant, t(74.4904527) = -1.6334224, p = 0.107.
Influence of CATI Scores on Accuracy
##
## Shapiro-Wilk normality test
##
## data: AccuracyCATI$Diff_ProportionCorrect[0:5000]
## W = 0.62301, p-value = 2.676e-16##
## Shapiro-Wilk normality test
##
## data: AccuracyCATI$CATI[0:5000]
## W = 0.99113, p-value = 0.6155## [1] 3.7e-24## [1] 0.4711401
## CATI Diff_ProportionCorrect
## CATI 1.00000000 -0.05435454
## Diff_ProportionCorrect -0.05435454 1.00000000
##
## Spearman's rank correlation rho
##
## data: AccuracyCATI$Diff_ProportionCorrect and AccuracyCATI$CATI
## S = 320188, p-value = 0.7216
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
## rho
## -0.03245308
Accuracy Summary
## `summarise()` has grouped output by 'Belief'. You can override using the
## `.groups` argument.## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUEOvert Attention
Plot
Generalised Linear Mixed Effect Model for Responder Overt Attention
| Estimate | Std. Error | z value | Pr(>|z|) | |
|---|---|---|---|---|
| (Intercept) | -0.119 | 0.292 | -0.406 | 0.684 |
| CongruencyIncongruent | 1.029 | 0.182 | 5.663 | 0.000 |
| BeliefHuman | 0.598 | 0.378 | 1.582 | 0.114 |
| AvatarRobot | 0.578 | 0.105 | 5.498 | 0.000 |
| CongruencyIncongruent:BeliefHuman | -0.022 | 0.202 | -0.111 | 0.912 |
| CongruencyIncongruent:AvatarRobot | 0.015 | 0.221 | 0.067 | 0.946 |
| BeliefHuman:AvatarRobot | -0.144 | 0.137 | -1.052 | 0.293 |
| CongruencyIncongruent:BeliefHuman:AvatarRobot | -0.153 | 0.296 | -0.517 | 0.605 |
## (Intercept)
## -0.11883371
## CongruencyIncongruent
## 1.02940923
## BeliefHuman
## 0.59819149
## AvatarRobot
## 0.57784605
## CongruencyIncongruent:BeliefHuman
## -0.02234746
## CongruencyIncongruent:AvatarRobot
## 0.01489097
## BeliefHuman:AvatarRobot
## -0.14438411
## CongruencyIncongruent:BeliefHuman:AvatarRobot
## -0.15327107## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula:
## PredictiveGazeFace ~ Congruency + Belief + Avatar + Congruency:Belief +
## Congruency:Avatar + Belief:Avatar + Congruency:Belief:Avatar +
## (1 | SubjectID) + (1 | TrialID)
## Data: UseableData
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
##
## AIC BIC logLik deviance df.resid
## 7314.1 7383.1 -3647.1 7294.1 7317
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.2636 -0.5737 0.3112 0.5663 7.1014
##
## Random effects:
## Groups Name Variance Std.Dev.
## TrialID (Intercept) 0.1407 0.3751
## SubjectID (Intercept) 2.0842 1.4437
## Number of obs: 7327, groups: TrialID, 72; SubjectID, 64
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) -0.11883 0.29242 -0.406
## CongruencyIncongruent 1.02941 0.18177 5.663
## BeliefHuman 0.59819 0.37812 1.582
## AvatarRobot 0.57785 0.10510 5.498
## CongruencyIncongruent:BeliefHuman -0.02235 0.20184 -0.111
## CongruencyIncongruent:AvatarRobot 0.01489 0.22099 0.067
## BeliefHuman:AvatarRobot -0.14438 0.13728 -1.052
## CongruencyIncongruent:BeliefHuman:AvatarRobot -0.15327 0.29627 -0.517
## Pr(>|z|)
## (Intercept) 0.684
## CongruencyIncongruent 1.49e-08 ***
## BeliefHuman 0.114
## AvatarRobot 3.84e-08 ***
## CongruencyIncongruent:BeliefHuman 0.912
## CongruencyIncongruent:AvatarRobot 0.946
## BeliefHuman:AvatarRobot 0.293
## CongruencyIncongruent:BeliefHuman:AvatarRobot 0.605
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) CngrnI BlfHmn AvtrRb CnI:BH CnI:AR BlH:AR
## CngrncyIncn -0.144
## BeliefHuman -0.750 0.074
## AvatarRobot -0.168 0.275 0.130
## CngrncyI:BH 0.086 -0.615 -0.112 -0.247
## CngrncyI:AR 0.075 -0.553 -0.058 -0.452 0.499
## BlfHmn:AvtR 0.128 -0.210 -0.167 -0.765 0.316 0.346
## CngrI:BH:AR -0.056 0.412 0.073 0.337 -0.671 -0.746 -0.445## We fitted a logistic mixed model (estimated using ML and BOBYQA optimizer) to
## predict PredictiveGazeFace with Congruency, Belief and Avatar (formula:
## PredictiveGazeFace ~ Congruency + Belief + Avatar + Congruency:Belief +
## Congruency:Avatar + Belief:Avatar + Congruency:Belief:Avatar). The model
## included SubjectID as random effects (formula: list(~1 | SubjectID, ~1 |
## TrialID)). The model's total explanatory power is substantial (conditional R2 =
## 0.43) and the part related to the fixed effects alone (marginal R2) is of 0.05.
## The model's intercept, corresponding to Congruency = Congruent, Belief = AI and
## Avatar = Anthropomorphic, is at -0.12 (95% CI [-0.69, 0.45], p = 0.684). Within
## this model:
##
## - The effect of Congruency [Incongruent] is statistically significant and
## positive (beta = 1.03, 95% CI [0.67, 1.39], p < .001; Std. beta = 1.03, 95% CI
## [0.67, 1.39])
## - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.60, 95% CI [-0.14, 1.34], p = 0.114; Std. beta = 0.60, 95% CI [-0.14,
## 1.34])
## - The effect of Avatar [Robot] is statistically significant and positive (beta
## = 0.58, 95% CI [0.37, 0.78], p < .001; Std. beta = 0.58, 95% CI [0.37, 0.78])
## - The effect of Congruency [Incongruent] × Belief [Human] is statistically
## non-significant and negative (beta = -0.02, 95% CI [-0.42, 0.37], p = 0.912;
## Std. beta = -0.02, 95% CI [-0.42, 0.37])
## - The effect of Congruency [Incongruent] × Avatar [Robot] is statistically
## non-significant and positive (beta = 0.01, 95% CI [-0.42, 0.45], p = 0.946;
## Std. beta = 0.01, 95% CI [-0.42, 0.45])
## - The effect of Belief [Human] × Avatar [Robot] is statistically
## non-significant and negative (beta = -0.14, 95% CI [-0.41, 0.12], p = 0.293;
## Std. beta = -0.14, 95% CI [-0.41, 0.12])
## - The effect of (Congruency [Incongruent] × Belief [Human]) × Avatar [Robot] is
## statistically non-significant and negative (beta = -0.15, 95% CI [-0.73, 0.43],
## p = 0.605; Std. beta = -0.15, 95% CI [-0.73, 0.43])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald z-distribution approximation.## The model included SubjectID as random effects (formula: list(~1 | SubjectID, ~1 | TrialID))## [1] "very strong evidence against"
## (Rules: jeffreys1961)## [1] 0.01333238## [1] 0.01333238## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] TRUE## [1] TRUE## [1] FALSE## [1] TRUE## [1] TRUE## [1] FALSE## [1] FALSE## [1] FALSE## [1] FALSE## [1] FALSE## [1] FALSE## [1] FALSE## [1] FALSE## [1] FALSE## [1] FALSE## [1] TRUEInfluence of CATI Scores on Overt Attention
##
## Shapiro-Wilk normality test
##
## data: PredictiveGazeFaceCATI$Diff_PredictiveGazeFaceMean[0:5000]
## W = 0.9649, p-value = 0.002602##
## Shapiro-Wilk normality test
##
## data: PredictiveGazeFaceCATI$CATI[0:5000]
## W = 0.99113, p-value = 0.6155## [1] 0.001458021## [1] 0.4711401
## CATI Diff_PredictiveGazeFaceMean
## CATI 1.0000000 -0.1264442
## Diff_PredictiveGazeFaceMean -0.1264442 1.0000000
##
## Spearman's rank correlation rho
##
## data: PredictiveGazeFaceCATI$Diff_PredictiveGazeFaceMean and PredictiveGazeFaceCATI$CATI
## S = 359087, p-value = 0.1498
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
## rho
## -0.1300937
Overt Attention Summary
## [1] TRUE## [1] TRUESaccadic Reaction Time (SRT)
Plot
Load Data and Identify Factors
All Trials
## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.
## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.
## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.
## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.
Overt Attention Trials Only
## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.
No Overt Attention Trials Only
## Coordinate system already present. Adding new coordinate system, which will
## replace the existing one.
Linear Mixed Effects Models
Load Data and Identify Factors
All Trials
| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | 449.525 | 16.667 | 125.270 | 26.971 | 0.000 |
| CongruencyIncongruent | 70.442 | 25.999 | 97.872 | 2.709 | 0.008 |
| BeliefHuman | 25.317 | 15.835 | 61.794 | 1.599 | 0.115 |
| AvatarRobot | 65.592 | 13.405 | 61.246 | 4.893 | 0.000 |
| CongruencyIncongruent:BeliefHuman | -2.543 | 16.134 | 61.278 | -0.158 | 0.875 |
| CongruencyIncongruent:AvatarRobot | -23.568 | 17.583 | 62.348 | -1.340 | 0.185 |
| BeliefHuman:AvatarRobot | 20.722 | 17.230 | 59.677 | 1.203 | 0.234 |
| CongruencyIncongruent:BeliefHuman:AvatarRobot | 3.561 | 22.752 | 60.966 | 0.157 | 0.876 |
## (Intercept)
## 449.524721
## CongruencyIncongruent
## 70.442123
## BeliefHuman
## 25.317308
## AvatarRobot
## 65.591614
## CongruencyIncongruent:BeliefHuman
## -2.543341
## CongruencyIncongruent:AvatarRobot
## -23.567755
## BeliefHuman:AvatarRobot
## 20.721743
## CongruencyIncongruent:BeliefHuman:AvatarRobot
## 3.561040
| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | 20.510 | 0.293 | 127.491 | 70.033 | 0.000 |
| CongruencyIncongruent | 1.183 | 0.453 | 90.113 | 2.612 | 0.011 |
| BeliefHuman | 0.434 | 0.271 | 61.993 | 1.602 | 0.114 |
| AvatarRobot | 0.986 | 0.204 | 61.755 | 4.831 | 0.000 |
| CongruencyIncongruent:BeliefHuman | -0.030 | 0.241 | 61.462 | -0.126 | 0.900 |
| CongruencyIncongruent:AvatarRobot | -0.406 | 0.261 | 62.021 | -1.554 | 0.125 |
| BeliefHuman:AvatarRobot | 0.346 | 0.262 | 60.216 | 1.322 | 0.191 |
| CongruencyIncongruent:BeliefHuman:AvatarRobot | -0.013 | 0.338 | 60.721 | -0.038 | 0.970 |
## (Intercept)
## 20.50990171
## CongruencyIncongruent
## 1.18321626
## BeliefHuman
## 0.43398897
## AvatarRobot
## 0.98605884
## CongruencyIncongruent:BeliefHuman
## -0.03036783
## CongruencyIncongruent:AvatarRobot
## -0.40594273
## BeliefHuman:AvatarRobot
## 0.34631018
## CongruencyIncongruent:BeliefHuman:AvatarRobot
## -0.01288491## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## SRTtf ~ Congruency + Belief + Avatar + Congruency:Belief + Congruency:Avatar +
## Belief:Avatar + Congruency:Belief:Avatar + (0 + Congruency +
## Avatar + Congruency:Avatar | SubjectID) + (1 | TrialID)
## Data: SRTData
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
##
## REML criterion at convergence: 27621.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.8040 -0.5996 -0.0064 0.5840 7.1527
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## TrialID (Intercept) 2.2968 1.5155
## SubjectID CongruencyCongruent 0.9437 0.9714
## CongruencyIncongruent 1.3258 1.1514 0.92
## AvatarRobot 0.6296 0.7935 -0.04 0.09
## CongruencyIncongruent:AvatarRobot 0.3683 0.6069 -0.45 -0.55
## Residual 5.8429 2.4172
##
##
##
##
##
## -0.39
##
## Number of obs: 5885, groups: TrialID, 72; SubjectID, 64
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 20.50990 0.29286 127.49130
## CongruencyIncongruent 1.18322 0.45308 90.11270
## BeliefHuman 0.43399 0.27086 61.99300
## AvatarRobot 0.98606 0.20411 61.75516
## CongruencyIncongruent:BeliefHuman -0.03037 0.24109 61.46155
## CongruencyIncongruent:AvatarRobot -0.40594 0.26127 62.02111
## BeliefHuman:AvatarRobot 0.34631 0.26205 60.21595
## CongruencyIncongruent:BeliefHuman:AvatarRobot -0.01288 0.33769 60.72099
## t value Pr(>|t|)
## (Intercept) 70.033 < 2e-16 ***
## CongruencyIncongruent 2.612 0.0106 *
## BeliefHuman 1.602 0.1142
## AvatarRobot 4.831 9.34e-06 ***
## CongruencyIncongruent:BeliefHuman -0.126 0.9002
## CongruencyIncongruent:AvatarRobot -1.554 0.1253
## BeliefHuman:AvatarRobot 1.322 0.1913
## CongruencyIncongruent:BeliefHuman:AvatarRobot -0.038 0.9697
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) CngrnI BlfHmn AvtrRb CnI:BH CnI:AR BlH:AR
## CngrncyIncn -0.350
## BeliefHuman -0.543 0.031
## AvatarRobot -0.151 0.123 0.162
## CngrncyI:BH 0.054 -0.318 -0.092 -0.231
## CngrncyI:AR -0.040 -0.263 0.043 -0.410 0.493
## BlfHmn:AvtR 0.117 -0.096 -0.204 -0.779 0.300 0.319
## CngrI:BH:AR 0.031 0.203 -0.064 0.317 -0.637 -0.773 -0.408## We fitted a linear mixed model (estimated using REML and BOBYQA optimizer) to
## predict SRTtf with Congruency, Belief and Avatar (formula: SRTtf ~ Congruency +
## Belief + Avatar + Congruency:Belief + Congruency:Avatar + Belief:Avatar +
## Congruency:Belief:Avatar). The model included Congruency as random effects
## (formula: list(~0 + Congruency + Avatar + Congruency:Avatar | SubjectID, ~1 |
## TrialID)). The model's total explanatory power is substantial (conditional R2 =
## 0.37) and the part related to the fixed effects alone (marginal R2) is of 0.06.
## The model's intercept, corresponding to Congruency = Congruent, Belief = AI and
## Avatar = Anthropomorphic, is at 20.51 (95% CI [19.94, 21.08], t(5865) = 70.03,
## p < .001). Within this model:
##
## - The effect of Congruency [Incongruent] is statistically significant and
## positive (beta = 1.18, 95% CI [0.30, 2.07], t(5865) = 2.61, p = 0.009; Std.
## beta = 0.39, 95% CI [0.10, 0.68])
## - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.43, 95% CI [-0.10, 0.96], t(5865) = 1.60, p = 0.109; Std. beta =
## 0.14, 95% CI [-0.03, 0.32])
## - The effect of Avatar [Robot] is statistically significant and positive (beta
## = 0.99, 95% CI [0.59, 1.39], t(5865) = 4.83, p < .001; Std. beta = 0.32, 95% CI
## [0.19, 0.46])
## - The effect of Congruency [Incongruent] × Belief [Human] is statistically
## non-significant and negative (beta = -0.03, 95% CI [-0.50, 0.44], t(5865) =
## -0.13, p = 0.900; Std. beta = -0.01, 95% CI [-0.17, 0.15])
## - The effect of Congruency [Incongruent] × Avatar [Robot] is statistically
## non-significant and negative (beta = -0.41, 95% CI [-0.92, 0.11], t(5865) =
## -1.55, p = 0.120; Std. beta = -0.13, 95% CI [-0.30, 0.03])
## - The effect of Belief [Human] × Avatar [Robot] is statistically
## non-significant and positive (beta = 0.35, 95% CI [-0.17, 0.86], t(5865) =
## 1.32, p = 0.186; Std. beta = 0.11, 95% CI [-0.06, 0.28])
## - The effect of (Congruency [Incongruent] × Belief [Human]) × Avatar [Robot] is
## statistically non-significant and negative (beta = -0.01, 95% CI [-0.67, 0.65],
## t(5865) = -0.04, p = 0.970; Std. beta = -4.24e-03, 95% CI [-0.22, 0.21])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.## The model included Congruency as random effects (formula: list(~0 + Congruency + Avatar + Congruency:Avatar | SubjectID, ~1 | TrialID))## [1] "very strong evidence against"
## (Rules: jeffreys1961)## [1] 0.0109985## [1] 0.0109985## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUEIndependent Samples t-Test (SRTtf by Avatar)
The mean SRTtf for the anthropomorphic avatar was 21.396 (SD = 2.754), whereas the mean for the robot avatar was 22.359 (SD = 3.227). A Welch two-samples t-test showed that the difference was statistically not significant, t(5723.4945917) = -12.3140331, p = 2.07^{-34}.
ANOVA (SRTtf by Avatar)
## Df Sum Sq Mean Sq F value Pr(>F)
## Avatar 1 1366 1366 151.9 <2e-16 ***
## Residuals 5883 52896 9
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## Shapiro-Wilk normality test
##
## data: aov_residuals[0:5000]
## W = 0.9889, p-value < 2.2e-16##
## Kruskal-Wallis rank sum test
##
## data: SRTtf by Avatar
## Kruskal-Wallis chi-squared = 208.45, df = 1, p-value < 2.2e-16## [1] TRUE## [1] TRUEIndependent Samples t-Test (SRTtf Difference by Avatar)
The mean SRTtf Difference between congruent and incongruent trials for the anthropomorphic group was -1.112 (SD = 0.955), whereas the mean difference for the robot avatar was -0.772 (SD = 1.155). A Welch two-samples t-test showed that the difference was statistically not significant, t(116.4019224) = -1.7868517, p = 0.0766.
ANOVA (SRTtf Difference by Avatar)
## Bin width defaults to 1/30 of the range of the data. Pick better value with
## `binwidth`.
## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?
## Bin width defaults to 1/30 of the range of the data. Pick better value with
## `binwidth`.
## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?## Df Sum Sq Mean Sq F value Pr(>F)
## Avatar 1 3.6 3.597 3.212 0.0756 .
## Residuals 122 136.6 1.120
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## Shapiro-Wilk normality test
##
## data: aov_residuals[0:5000]
## W = 0.98877, p-value = 0.4067##
## Kruskal-Wallis rank sum test
##
## data: SRTtfDiff by Avatar
## Kruskal-Wallis chi-squared = 3.7124, df = 1, p-value = 0.05401## [1] TRUE## [1] TRUEAvatar (Robot)
| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | 505.048 | 21.926 | 111.486 | 23.035 | 0.000 |
| CongruencyIncongruent | 48.358 | 29.476 | 85.564 | 1.641 | 0.105 |
| BeliefHuman | 54.343 | 22.533 | 59.246 | 2.412 | 0.019 |
| CongruencyIncongruent:BeliefHuman | -0.545 | 16.485 | 54.215 | -0.033 | 0.974 |
## (Intercept) CongruencyIncongruent
## 505.0477092 48.3578383
## BeliefHuman CongruencyIncongruent:BeliefHuman
## 54.3428603 -0.5446473
| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | 43.044 | 0.978 | 118.299 | 44.028 | 0.000 |
| CongruencyIncongruent | 2.201 | 1.395 | 83.753 | 1.578 | 0.118 |
| BeliefHuman | 2.453 | 0.954 | 59.256 | 2.571 | 0.013 |
| CongruencyIncongruent:BeliefHuman | -0.175 | 0.714 | 54.201 | -0.244 | 0.808 |
## (Intercept) CongruencyIncongruent
## 43.0442716 2.2013746
## BeliefHuman CongruencyIncongruent:BeliefHuman
## 2.4528081 -0.1745263## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: SRTtf ~ Congruency + Belief + Congruency:Belief + (0 + Congruency |
## SubjectID) + (1 | TrialID)
## Data: SRTData_Robot
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
##
## REML criterion at convergence: 20011.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5470 -0.5971 -0.0048 0.5691 7.2472
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## TrialID (Intercept) 22.11 4.702
## SubjectID CongruencyCongruent 11.73 3.425
## CongruencyIncongruent 10.27 3.205 0.91
## Residual 48.02 6.930
## Number of obs: 2928, groups: TrialID, 72; SubjectID, 61
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 43.0443 0.9777 118.2988 44.028 <2e-16
## CongruencyIncongruent 2.2014 1.3951 83.7531 1.578 0.1184
## BeliefHuman 2.4528 0.9541 59.2564 2.571 0.0127
## CongruencyIncongruent:BeliefHuman -0.1745 0.7141 54.2014 -0.244 0.8078
##
## (Intercept) ***
## CongruencyIncongruent
## BeliefHuman *
## CongruencyIncongruent:BeliefHuman
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) CngrnI BlfHmn
## CngrncyIncn -0.398
## BeliefHuman -0.584 0.100
## CngrncyI:BH 0.190 -0.307 -0.321## We fitted a linear mixed model (estimated using REML and BOBYQA optimizer) to
## predict SRTtf with Congruency and Belief (formula: SRTtf ~ Congruency + Belief
## + Congruency:Belief). The model included Congruency as random effects (formula:
## list(~0 + Congruency | SubjectID, ~1 | TrialID)). The model's total explanatory
## power is substantial (conditional R2 = 0.36) and the part related to the fixed
## effects alone (marginal R2) is of 0.03. The model's intercept, corresponding to
## Congruency = Congruent and Belief = AI, is at 43.04 (95% CI [41.13, 44.96],
## t(2919) = 44.03, p < .001). Within this model:
##
## - The effect of Congruency [Incongruent] is statistically non-significant and
## positive (beta = 2.20, 95% CI [-0.53, 4.94], t(2919) = 1.58, p = 0.115; Std.
## beta = 0.25, 95% CI [-0.06, 0.56])
## - The effect of Belief [Human] is statistically significant and positive (beta
## = 2.45, 95% CI [0.58, 4.32], t(2919) = 2.57, p = 0.010; Std. beta = 0.28, 95%
## CI [0.07, 0.49])
## - The effect of Congruency [Incongruent] × Belief [Human] is statistically
## non-significant and negative (beta = -0.17, 95% CI [-1.57, 1.23], t(2919) =
## -0.24, p = 0.807; Std. beta = -0.02, 95% CI [-0.18, 0.14])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.## The model included Congruency as random effects (formula: list(~0 + Congruency | SubjectID, ~1 | TrialID))## [1] "strong evidence against"
## (Rules: jeffreys1961)## [1] 0.03397302## [1] 0.03397302## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] FALSE## [1] TRUEAvatar (Anthropomorphic)
| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | 458.136 | 15.411 | 110.995 | 29.728 | 0.000 |
| CongruencyIncongruent | 67.924 | 22.516 | 96.398 | 3.017 | 0.003 |
| BeliefHuman | 23.432 | 15.841 | 60.472 | 1.479 | 0.144 |
| CongruencyIncongruent:BeliefHuman | -0.470 | 15.948 | 60.663 | -0.029 | 0.977 |
## (Intercept) CongruencyIncongruent
## 458.1359973 67.9235289
## BeliefHuman CongruencyIncongruent:BeliefHuman
## 23.4315188 -0.4698318
| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | 12.883 | 0.129 | 115.665 | 99.940 | 0.000 |
| CongruencyIncongruent | 0.548 | 0.186 | 87.609 | 2.951 | 0.004 |
| BeliefHuman | 0.192 | 0.129 | 60.594 | 1.488 | 0.142 |
| CongruencyIncongruent:BeliefHuman | -0.003 | 0.110 | 61.912 | -0.026 | 0.980 |
## (Intercept) CongruencyIncongruent
## 12.88259629 0.54770443
## BeliefHuman CongruencyIncongruent:BeliefHuman
## 0.19173801 -0.00281953## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: SRTtf ~ Congruency + Belief + Congruency:Belief + (0 + Congruency |
## SubjectID) + (1 | TrialID)
## Data: SRTData_Anthropomorphic
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
##
## REML criterion at convergence: 9168.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.8812 -0.6009 -0.0038 0.5994 6.7588
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## TrialID (Intercept) 0.3641 0.6034
## SubjectID CongruencyCongruent 0.2152 0.4639
## CongruencyIncongruent 0.2763 0.5257 0.90
## Residual 1.1548 1.0746
## Number of obs: 2957, groups: TrialID, 72; SubjectID, 63
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 12.88260 0.12890 115.66456 99.940
## CongruencyIncongruent 0.54770 0.18558 87.60900 2.951
## BeliefHuman 0.19174 0.12883 60.59411 1.488
## CongruencyIncongruent:BeliefHuman -0.00282 0.11042 61.91179 -0.026
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## CongruencyIncongruent 0.00406 **
## BeliefHuman 0.14185
## CongruencyIncongruent:BeliefHuman 0.97971
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) CngrnI BlfHmn
## CngrncyIncn -0.333
## BeliefHuman -0.591 0.049
## CngrncyI:BH 0.083 -0.357 -0.134## We fitted a linear mixed model (estimated using REML and BOBYQA optimizer) to
## predict SRTtf with Congruency and Belief (formula: SRTtf ~ Congruency + Belief
## + Congruency:Belief). The model included Congruency as random effects (formula:
## list(~0 + Congruency | SubjectID, ~1 | TrialID)). The model's total explanatory
## power is substantial (conditional R2 = 0.30) and the part related to the fixed
## effects alone (marginal R2) is of 0.04. The model's intercept, corresponding to
## Congruency = Congruent and Belief = AI, is at 12.88 (95% CI [12.63, 13.14],
## t(2948) = 99.94, p < .001). Within this model:
##
## - The effect of Congruency [Incongruent] is statistically significant and
## positive (beta = 0.55, 95% CI [0.18, 0.91], t(2948) = 2.95, p = 0.003; Std.
## beta = 0.42, 95% CI [0.14, 0.70])
## - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.19, 95% CI [-0.06, 0.44], t(2948) = 1.49, p = 0.137; Std. beta =
## 0.15, 95% CI [-0.05, 0.34])
## - The effect of Congruency [Incongruent] × Belief [Human] is statistically
## non-significant and negative (beta = -2.82e-03, 95% CI [-0.22, 0.21], t(2948) =
## -0.03, p = 0.980; Std. beta = -2.16e-03, 95% CI [-0.17, 0.16])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.## The model included Congruency as random effects (formula: list(~0 + Congruency | SubjectID, ~1 | TrialID))## [1] "extreme evidence against"
## (Rules: jeffreys1961)## [1] 0.005071679## [1] 0.005071679## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] FALSE## [1] TRUEOvert Attention Trials Only
| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | 450.413 | 17.736 | 122.595 | 25.395 | 0.000 |
| CongruencyIncongruent | 75.288 | 26.558 | 104.899 | 2.835 | 0.006 |
| BeliefHuman | 22.674 | 17.691 | 61.766 | 1.282 | 0.205 |
| AvatarRobot | 69.827 | 14.334 | 63.513 | 4.872 | 0.000 |
| CongruencyIncongruent:BeliefHuman | -0.689 | 18.273 | 56.415 | -0.038 | 0.970 |
| CongruencyIncongruent:AvatarRobot | -30.590 | 19.538 | 59.741 | -1.566 | 0.123 |
| BeliefHuman:AvatarRobot | 19.824 | 18.160 | 59.819 | 1.092 | 0.279 |
| CongruencyIncongruent:BeliefHuman:AvatarRobot | 5.604 | 24.879 | 56.890 | 0.225 | 0.823 |
## (Intercept)
## 450.4133454
## CongruencyIncongruent
## 75.2880384
## BeliefHuman
## 22.6740467
## AvatarRobot
## 69.8269011
## CongruencyIncongruent:BeliefHuman
## -0.6893588
## CongruencyIncongruent:AvatarRobot
## -30.5904151
## BeliefHuman:AvatarRobot
## 19.8238492
## CongruencyIncongruent:BeliefHuman:AvatarRobot
## 5.6042587
| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | 24.205 | 0.401 | 123.551 | 60.378 | 0.000 |
| CongruencyIncongruent | 1.615 | 0.591 | 97.879 | 2.734 | 0.007 |
| BeliefHuman | 0.519 | 0.394 | 60.573 | 1.319 | 0.192 |
| AvatarRobot | 1.367 | 0.282 | 63.065 | 4.847 | 0.000 |
| CongruencyIncongruent:BeliefHuman | 0.001 | 0.361 | 54.318 | 0.003 | 0.998 |
| CongruencyIncongruent:AvatarRobot | -0.616 | 0.385 | 58.530 | -1.601 | 0.115 |
| BeliefHuman:AvatarRobot | 0.442 | 0.357 | 59.360 | 1.239 | 0.220 |
| CongruencyIncongruent:BeliefHuman:AvatarRobot | -0.043 | 0.490 | 55.725 | -0.087 | 0.931 |
## (Intercept)
## 24.204691709
## CongruencyIncongruent
## 1.615132343
## BeliefHuman
## 0.519332902
## AvatarRobot
## 1.367125657
## CongruencyIncongruent:BeliefHuman
## 0.001036391
## CongruencyIncongruent:AvatarRobot
## -0.616454267
## BeliefHuman:AvatarRobot
## 0.441909681
## CongruencyIncongruent:BeliefHuman:AvatarRobot
## -0.042514925## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## SRTtf ~ Congruency + Belief + Avatar + Congruency:Belief + Congruency:Avatar +
## Belief:Avatar + Congruency:Belief:Avatar + (0 + Congruency +
## Avatar + Congruency:Avatar | SubjectID) + (1 | TrialID)
## Data: SRTDataOA
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
##
## REML criterion at convergence: 22073.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.4662 -0.6065 -0.0091 0.5975 6.7734
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## TrialID (Intercept) 3.6111 1.9003
## SubjectID CongruencyCongruent 1.7448 1.3209
## CongruencyIncongruent 2.1894 1.4797 0.91
## AvatarRobot 0.7968 0.8926 -0.01 0.07
## CongruencyIncongruent:AvatarRobot 0.5326 0.7298 -0.47 -0.52
## Residual 9.6594 3.1080
##
##
##
##
##
## -0.30
##
## Number of obs: 4235, groups: TrialID, 72; SubjectID, 64
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 24.204692 0.400888 123.550678
## CongruencyIncongruent 1.615132 0.590787 97.878588
## BeliefHuman 0.519333 0.393785 60.572526
## AvatarRobot 1.367126 0.282030 63.065353
## CongruencyIncongruent:BeliefHuman 0.001036 0.361346 54.318432
## CongruencyIncongruent:AvatarRobot -0.616454 0.385085 58.529947
## BeliefHuman:AvatarRobot 0.441910 0.356551 59.360323
## CongruencyIncongruent:BeliefHuman:AvatarRobot -0.042515 0.489600 55.725207
## t value Pr(>|t|)
## (Intercept) 60.378 < 2e-16 ***
## CongruencyIncongruent 2.734 0.00743 **
## BeliefHuman 1.319 0.19219
## AvatarRobot 4.847 8.51e-06 ***
## CongruencyIncongruent:BeliefHuman 0.003 0.99772
## CongruencyIncongruent:AvatarRobot -1.601 0.11480
## BeliefHuman:AvatarRobot 1.239 0.22008
## CongruencyIncongruent:BeliefHuman:AvatarRobot -0.087 0.93111
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) CngrnI BlfHmn AvtrRb CnI:BH CnI:AR BlH:AR
## CngrncyIncn -0.370
## BeliefHuman -0.593 0.089
## AvatarRobot -0.221 0.151 0.224
## CngrncyI:BH 0.143 -0.381 -0.221 -0.247
## CngrncyI:AR 0.021 -0.305 -0.021 -0.432 0.498
## BlfHmn:AvtR 0.174 -0.119 -0.270 -0.790 0.305 0.341
## CngrI:BH:AR -0.016 0.240 0.009 0.339 -0.626 -0.786 -0.425## We fitted a linear mixed model (estimated using REML and BOBYQA optimizer) to
## predict SRTtf with Congruency, Belief and Avatar (formula: SRTtf ~ Congruency +
## Belief + Avatar + Congruency:Belief + Congruency:Avatar + Belief:Avatar +
## Congruency:Belief:Avatar). The model included Congruency as random effects
## (formula: list(~0 + Congruency + Avatar + Congruency:Avatar | SubjectID, ~1 |
## TrialID)). The model's total explanatory power is substantial (conditional R2 =
## 0.36) and the part related to the fixed effects alone (marginal R2) is of 0.07.
## The model's intercept, corresponding to Congruency = Congruent, Belief = AI and
## Avatar = Anthropomorphic, is at 24.20 (95% CI [23.42, 24.99], t(4215) = 60.38,
## p < .001). Within this model:
##
## - The effect of Congruency [Incongruent] is statistically significant and
## positive (beta = 1.62, 95% CI [0.46, 2.77], t(4215) = 2.73, p = 0.006; Std.
## beta = 0.41, 95% CI [0.11, 0.70])
## - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.52, 95% CI [-0.25, 1.29], t(4215) = 1.32, p = 0.187; Std. beta =
## 0.13, 95% CI [-0.06, 0.32])
## - The effect of Avatar [Robot] is statistically significant and positive (beta
## = 1.37, 95% CI [0.81, 1.92], t(4215) = 4.85, p < .001; Std. beta = 0.34, 95% CI
## [0.20, 0.48])
## - The effect of Congruency [Incongruent] × Belief [Human] is statistically
## non-significant and positive (beta = 1.04e-03, 95% CI [-0.71, 0.71], t(4215) =
## 2.87e-03, p = 0.998; Std. beta = 2.60e-04, 95% CI [-0.18, 0.18])
## - The effect of Congruency [Incongruent] × Avatar [Robot] is statistically
## non-significant and negative (beta = -0.62, 95% CI [-1.37, 0.14], t(4215) =
## -1.60, p = 0.109; Std. beta = -0.15, 95% CI [-0.34, 0.03])
## - The effect of Belief [Human] × Avatar [Robot] is statistically
## non-significant and positive (beta = 0.44, 95% CI [-0.26, 1.14], t(4215) =
## 1.24, p = 0.215; Std. beta = 0.11, 95% CI [-0.06, 0.29])
## - The effect of (Congruency [Incongruent] × Belief [Human]) × Avatar [Robot] is
## statistically non-significant and negative (beta = -0.04, 95% CI [-1.00, 0.92],
## t(4215) = -0.09, p = 0.931; Std. beta = -0.01, 95% CI [-0.25, 0.23])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.## The model included Congruency as random effects (formula: list(~0 + Congruency + Avatar + Congruency:Avatar | SubjectID, ~1 | TrialID))## [1] "very strong evidence against"
## (Rules: jeffreys1961)## [1] 0.01885772## [1] 0.01885772## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUENo Overt Attention Trials Only
## fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients## boundary (singular) fit: see help('isSingular')## fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients
| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | 419.776 | 56.437 | 29.786 | 7.438 | 0.000 |
| CongruencyIncongruent | 67.357 | 32.418 | 39.139 | 2.078 | 0.044 |
| BeliefHuman | 45.403 | 38.604 | 35.231 | 1.176 | 0.247 |
| AvatarRobot | 104.009 | 28.261 | 45.438 | 3.680 | 0.001 |
| CongruencyCongruent:BeliefAI:AvatarAnthropomorphic | 38.375 | 55.429 | 26.267 | 0.692 | 0.495 |
| CongruencyIncongruent:BeliefAI:AvatarAnthropomorphic | 23.621 | 40.228 | 46.868 | 0.587 | 0.560 |
| CongruencyCongruent:BeliefHuman:AvatarAnthropomorphic | 22.371 | 29.742 | 37.620 | 0.752 | 0.457 |
| CongruencyCongruent:BeliefAI:AvatarRobot | 3.086 | 34.206 | 16.548 | 0.090 | 0.929 |
## (Intercept)
## 419.776266
## CongruencyIncongruent
## 67.356673
## BeliefHuman
## 45.403465
## AvatarRobot
## 104.009093
## CongruencyCongruent:BeliefAI:AvatarAnthropomorphic
## 38.375114
## CongruencyIncongruent:BeliefAI:AvatarAnthropomorphic
## 23.621054
## CongruencyCongruent:BeliefHuman:AvatarAnthropomorphic
## 22.370758
## CongruencyCongruent:BeliefAI:AvatarRobot
## 3.085896
## fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients## boundary (singular) fit: see help('isSingular')## fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients
| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | 14.673 | 0.518 | 40.722 | 28.350 | 0.000 |
| CongruencyIncongruent | 0.609 | 0.341 | 62.518 | 1.785 | 0.079 |
| BeliefHuman | 0.470 | 0.338 | 36.530 | 1.391 | 0.173 |
| AvatarRobot | 0.849 | 0.257 | 66.203 | 3.300 | 0.002 |
| CongruencyCongruent:BeliefAI:AvatarAnthropomorphic | 0.316 | 0.506 | 34.635 | 0.626 | 0.536 |
| CongruencyIncongruent:BeliefAI:AvatarAnthropomorphic | 0.292 | 0.365 | 69.804 | 0.798 | 0.427 |
| CongruencyCongruent:BeliefHuman:AvatarAnthropomorphic | 0.128 | 0.278 | 62.927 | 0.461 | 0.646 |
| CongruencyCongruent:BeliefAI:AvatarRobot | 0.099 | 0.322 | 23.368 | 0.308 | 0.761 |
## (Intercept)
## 14.67314213
## CongruencyIncongruent
## 0.60879729
## BeliefHuman
## 0.46985484
## AvatarRobot
## 0.84895192
## CongruencyCongruent:BeliefAI:AvatarAnthropomorphic
## 0.31631800
## CongruencyIncongruent:BeliefAI:AvatarAnthropomorphic
## 0.29169776
## CongruencyCongruent:BeliefHuman:AvatarAnthropomorphic
## 0.12835394
## CongruencyCongruent:BeliefAI:AvatarRobot
## 0.09919277## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: SRTtf ~ Congruency + Belief + Avatar + Congruency:Belief:Avatar +
## (0 + Congruency + Avatar + Congruency:Avatar | SubjectID) +
## (1 | TrialID)
## Data: SRTDataOANo
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
##
## REML criterion at convergence: 6151.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0248 -0.5575 0.0087 0.5492 6.3806
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## TrialID (Intercept) 0.8408 0.9170
## SubjectID CongruencyCongruent 0.3069 0.5540
## CongruencyIncongruent 0.2471 0.4971 0.87
## AvatarRobot 0.4004 0.6327 -0.23 0.16
## CongruencyIncongruent:AvatarRobot 0.1669 0.4085 0.17 0.03
## Residual 2.0432 1.4294
##
##
##
##
##
## -0.83
##
## Number of obs: 1650, groups: TrialID, 72; SubjectID, 64
##
## Fixed effects:
## Estimate Std. Error
## (Intercept) 14.67314 0.51758
## CongruencyIncongruent 0.60880 0.34113
## BeliefHuman 0.46985 0.33767
## AvatarRobot 0.84895 0.25723
## CongruencyCongruent:BeliefAI:AvatarAnthropomorphic 0.31632 0.50558
## CongruencyIncongruent:BeliefAI:AvatarAnthropomorphic 0.29170 0.36533
## CongruencyCongruent:BeliefHuman:AvatarAnthropomorphic 0.12835 0.27830
## CongruencyCongruent:BeliefAI:AvatarRobot 0.09919 0.32249
## df t value Pr(>|t|)
## (Intercept) 40.72183 28.350 < 2e-16
## CongruencyIncongruent 62.51847 1.785 0.07917
## BeliefHuman 36.52994 1.391 0.17250
## AvatarRobot 66.20328 3.300 0.00156
## CongruencyCongruent:BeliefAI:AvatarAnthropomorphic 34.63458 0.626 0.53564
## CongruencyIncongruent:BeliefAI:AvatarAnthropomorphic 69.80440 0.798 0.42731
## CongruencyCongruent:BeliefHuman:AvatarAnthropomorphic 62.92680 0.461 0.64624
## CongruencyCongruent:BeliefAI:AvatarRobot 23.36846 0.308 0.76113
##
## (Intercept) ***
## CongruencyIncongruent .
## BeliefHuman
## AvatarRobot **
## CongruencyCongruent:BeliefAI:AvatarAnthropomorphic
## CongruencyIncongruent:BeliefAI:AvatarAnthropomorphic
## CongruencyCongruent:BeliefHuman:AvatarAnthropomorphic
## CongruencyCongruent:BeliefAI:AvatarRobot
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) CngrnI BlfHmn AvtrRb CC:BAI:AA CI:BAI CC:BH:
## CngrncyIncn -0.588
## BeliefHuman -0.820 0.351
## AvatarRobot -0.783 0.422 0.509
## CngC:BAI:AA -0.932 0.506 0.794 0.802
## CngI:BAI:AA -0.787 0.300 0.722 0.701 0.820
## CngrC:BH:AA -0.731 0.487 0.374 0.809 0.750 0.568
## CngC:BAI:AR -0.767 0.457 0.734 0.461 0.793 0.647 0.529
## fit warnings:
## fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')## fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients## boundary (singular) fit: see help('isSingular')## fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients## Random effect variances not available. Returned R2 does not account for random effects.## fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients## boundary (singular) fit: see help('isSingular')## fixed-effect model matrix is rank deficient so dropping 4 columns / coefficients## Random effect variances not available. Returned R2 does not account for random effects.## We fitted a linear mixed model (estimated using REML and BOBYQA optimizer) to
## predict SRTtf with Congruency, Belief and Avatar (formula: SRTtf ~ Congruency +
## Belief + Avatar + Congruency:Belief:Avatar). The model included Congruency as
## random effects (formula: list(~0 + Congruency + Avatar + Congruency:Avatar |
## SubjectID, ~1 | TrialID)). The model's explanatory power related to the fixed
## effects alone (marginal R2) is 0.09. The model's intercept, corresponding to
## Congruency = Congruent, Belief = AI and Avatar = Anthropomorphic, is at 14.67
## (95% CI [13.66, 15.69], t(1630) = 28.35, p < .001). Within this model:
##
## - The effect of Congruency [Incongruent] is statistically non-significant and
## positive (beta = 0.61, 95% CI [-0.06, 1.28], t(1630) = 1.78, p = 0.075; Std.
## beta = 0.35, 95% CI [-0.03, 0.74])
## - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.47, 95% CI [-0.19, 1.13], t(1630) = 1.39, p = 0.164; Std. beta =
## 0.27, 95% CI [-0.11, 0.65])
## - The effect of Avatar [Robot] is statistically significant and positive (beta
## = 0.85, 95% CI [0.34, 1.35], t(1630) = 3.30, p < .001; Std. beta = 0.49, 95% CI
## [0.20, 0.78])
## - The effect of CongruencyCongruent × BeliefAI × AvatarAnthropomorphic is
## statistically non-significant and positive (beta = 0.32, 95% CI [-0.68, 1.31],
## t(1630) = 0.63, p = 0.532; Std. beta = 0.18, 95% CI [-0.39, 0.75])
## - The effect of Congruency [Incongruent] × BeliefAI × AvatarAnthropomorphic is
## statistically non-significant and positive (beta = 0.29, 95% CI [-0.42, 1.01],
## t(1630) = 0.80, p = 0.425; Std. beta = 0.17, 95% CI [-0.24, 0.58])
## - The effect of CongruencyCongruent × Belief [Human] × AvatarAnthropomorphic is
## statistically non-significant and positive (beta = 0.13, 95% CI [-0.42, 0.67],
## t(1630) = 0.46, p = 0.645; Std. beta = 0.07, 95% CI [-0.24, 0.39])
## - The effect of CongruencyCongruent × BeliefAI × Avatar [Robot] is
## statistically non-significant and positive (beta = 0.10, 95% CI [-0.53, 0.73],
## t(1630) = 0.31, p = 0.758; Std. beta = 0.06, 95% CI [-0.31, 0.42])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.## The model included Congruency as random effects (formula: list(~0 + Congruency + Avatar + Congruency:Avatar | SubjectID, ~1 | TrialID))## boundary (singular) fit: see help('isSingular')## [1] "extreme evidence against"
## (Rules: jeffreys1961)## [1] 7.505645e-08## [1] 7.505645e-08## boundary (singular) fit: see help('isSingular')## [1] "extreme evidence against"
## (Rules: jeffreys1961)## [1] 6.118933e-06## [1] 6.118933e-06## boundary (singular) fit: see help('isSingular')## [1] "extreme evidence against"
## (Rules: jeffreys1961)## [1] 6.118933e-06## [1] 6.118933e-06## boundary (singular) fit: see help('isSingular')## [1] "extreme evidence against"
## (Rules: jeffreys1961)## [1] 4.435249e-06## [1] 4.435249e-06## fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients## boundary (singular) fit: see help('isSingular')## fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)## [1] 1## [1] 1## fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients## boundary (singular) fit: see help('isSingular')## fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients## boundary (singular) fit: see help('isSingular')## fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUEInfluence of CATI Scores on SRT
##
## Shapiro-Wilk normality test
##
## data: SRTtfCATI$Diff_SRTtfMean[0:5000]
## W = 0.99154, p-value = 0.655##
## Shapiro-Wilk normality test
##
## data: SRTtfCATI$CATI[0:5000]
## W = 0.99113, p-value = 0.6155## [1] 0.5327362## [1] 0.4711401
## CATI Diff_SRTtfMean
## CATI 1.00000000 -0.07606236
## Diff_SRTtfMean -0.07606236 1.00000000
##
## Spearman's rank correlation rho
##
## data: SRTtfCATI$Diff_SRTtfMean and SRTtfCATI$CATI
## S = 350969, p-value = 0.2479
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
## rho
## -0.1045442
SRT Summary
All Trials
## `summarise()` has grouped output by 'Avatar'. You can override using the
## `.groups` argument.## [1] TRUE## [1] TRUEOvert Attention Trials Only
## `summarise()` has grouped output by 'Belief'. You can override using the
## `.groups` argument.## [1] TRUE## [1] TRUENo Overt Attention Trials Only
## `summarise()` has grouped output by 'Belief'. You can override using the
## `.groups` argument.## [1] TRUE## [1] TRUEInitiator Trials
## `summarise()` has grouped output by 'Belief'. You can override using the
## `.groups` argument.
## `summarise()` has grouped output by 'Belief'. You can override using the
## `.groups` argument.## `summarise()` has grouped output by 'Belief'. You can override using the
## `.groups` argument.
## `summarise()` has grouped output by 'Belief'. You can override using the
## `.groups` argument.## `summarise()` has grouped output by 'Belief'. You can override using the
## `.groups` argument.
## `summarise()` has grouped output by 'Belief'. You can override using the
## `.groups` argument.Accuracy
Plot
Generalised Linear Mixed Effect Model for Initiator Accuracy
| Estimate | Std. Error | z value | Pr(>|z|) | |
|---|---|---|---|---|
| (Intercept) | 7.101 | 1.074 | 6.614 | 0.000 |
| BeliefHuman | 0.692 | 1.029 | 0.672 | 0.502 |
| AvatarRobot | -1.885 | 1.115 | -1.690 | 0.091 |
| BeliefHuman:AvatarRobot | -0.644 | 1.168 | -0.551 | 0.582 |
## (Intercept) BeliefHuman AvatarRobot
## 7.1007093 0.6915022 -1.8847620
## BeliefHuman:AvatarRobot
## -0.6437033## Error in file(file, if (append) "a" else "w"): cannot open the connection## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: CorrectIncorrect ~ Belief + Avatar + Belief:Avatar + (1 + Belief +
## Avatar | SubjectID) + (1 | TrialID)
## Data: UseableData
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
##
## AIC BIC logLik deviance df.resid
## 924.6 1001.9 -451.3 902.6 8356
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -12.3777 0.0228 0.0594 0.0868 1.8279
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## TrialID (Intercept) 0.8156 0.9031
## SubjectID (Intercept) 6.7835 2.6045
## BeliefHuman 2.2803 1.5101 -0.19
## AvatarRobot 7.6515 2.7661 -0.98 0.00
## Number of obs: 8367, groups: TrialID, 72; SubjectID, 65
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 7.1007 1.0736 6.614 3.75e-11 ***
## BeliefHuman 0.6915 1.0292 0.672 0.5017
## AvatarRobot -1.8848 1.1155 -1.690 0.0911 .
## BeliefHuman:AvatarRobot -0.6437 1.1681 -0.551 0.5816
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlfHmn AvtrRb
## BeliefHuman -0.473
## AvatarRobot -0.938 0.490
## BlfHmn:AvtR 0.418 -0.912 -0.527## We fitted a logistic mixed model (estimated using ML and BOBYQA optimizer) to
## predict CorrectIncorrect with Belief and Avatar (formula: CorrectIncorrect ~
## Belief + Avatar + Belief:Avatar). The model included Belief as random effects
## (formula: list(~1 + Belief + Avatar | SubjectID, ~1 | TrialID)). The model's
## total explanatory power is substantial (conditional R2 = 0.65) and the part
## related to the fixed effects alone (marginal R2) is of 0.14. The model's
## intercept, corresponding to Belief = AI and Avatar = Anthropomorphic, is at
## 7.10 (95% CI [5.00, 9.21], p < .001). Within this model:
##
## - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.69, 95% CI [-1.33, 2.71], p = 0.502; Std. beta = 0.69, 95% CI [-1.33,
## 2.71])
## - The effect of Avatar [Robot] is statistically non-significant and negative
## (beta = -1.88, 95% CI [-4.07, 0.30], p = 0.091; Std. beta = -1.88, 95% CI
## [-4.07, 0.30])
## - The effect of Belief [Human] × Avatar [Robot] is statistically
## non-significant and negative (beta = -0.64, 95% CI [-2.93, 1.65], p = 0.582;
## Std. beta = -0.64, 95% CI [-2.93, 1.65])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald z-distribution approximation.## The model included Belief as random effects (formula: list(~1 + Belief + Avatar | SubjectID, ~1 | TrialID))## [1] "no evidence against or in favour of"
## (Rules: jeffreys1961)## [1] 1## Error in file(file, if (append) "a" else "w"): cannot open the connection## [1] 1## [1] "no evidence against or in favour of"
## (Rules: jeffreys1961)## [1] 1## Error in file(file, if (append) "a" else "w"): cannot open the connection## [1] 1## [1] "no evidence against or in favour of"
## (Rules: jeffreys1961)## [1] 1## Error in file(file, if (append) "a" else "w"): cannot open the connection## [1] 1## [1] FALSE## [1] FALSE## [1] FALSE## [1] FALSE## [1] FALSE## [1] FALSE## [1] FALSE## [1] FALSEAccuracy Summary
## [1] TRUE## [1] TRUEOvert Attention
Frequency of Initiator Overt Attention
Plot
Load Data and Identify Factors
Linear Mixed Effects Models
Load Data and Identify Factors
## boundary (singular) fit: see help('isSingular')
| Estimate | Std. Error | z value | Pr(>|z|) | |
|---|---|---|---|---|
| (Intercept) | 1.406 | 0.275 | 5.120 | 0.000 |
| BeliefHuman | 0.322 | 0.380 | 0.847 | 0.397 |
| AvatarRobot | 0.199 | 0.136 | 1.458 | 0.145 |
## (Intercept) BeliefHuman AvatarRobot
## 1.4061579 0.3215809 0.1986315## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: iOAFAll ~ Belief + Avatar + (1 + Belief + Avatar | SubjectID) +
## (1 + Belief | TrialID)
## Data: UseableInitData
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
##
## AIC BIC logLik deviance df.resid
## 7441.5 7525.7 -3708.7 7417.5 8252
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -8.1151 0.0907 0.3142 0.5037 2.0203
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## TrialID (Intercept) 0.000000 0.00000
## BeliefHuman 0.001356 0.03682 NaN
## SubjectID (Intercept) 2.069187 1.43847
## BeliefHuman 1.180184 1.08636 -0.14
## AvatarRobot 0.668626 0.81770 -0.37 -0.03
## Number of obs: 8264, groups: TrialID, 72; SubjectID, 65
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.4062 0.2746 5.120 3.05e-07 ***
## BeliefHuman 0.3216 0.3799 0.847 0.397
## AvatarRobot 0.1986 0.1363 1.458 0.145
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlfHmn
## BeliefHuman -0.667
## AvatarRobot -0.242 -0.056
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')## boundary (singular) fit: see help('isSingular')## Random effect variances not available. Returned R2 does not account for random effects.## boundary (singular) fit: see help('isSingular')## Random effect variances not available. Returned R2 does not account for random effects.## We fitted a logistic mixed model (estimated using ML and BOBYQA optimizer) to
## predict iOAFAll with Belief and Avatar (formula: iOAFAll ~ Belief + Avatar).
## The model included Belief as random effects (formula: list(~1 + Belief + Avatar
## | SubjectID, ~1 + Belief | TrialID)). The model's explanatory power related to
## the fixed effects alone (marginal R2) is 0.01. The model's intercept,
## corresponding to Belief = AI and Avatar = Anthropomorphic, is at 1.41 (95% CI
## [0.87, 1.94], p < .001). Within this model:
##
## - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.32, 95% CI [-0.42, 1.07], p = 0.397; Std. beta = 0.32, 95% CI [-0.42,
## 1.07])
## - The effect of Avatar [Robot] is statistically non-significant and positive
## (beta = 0.20, 95% CI [-0.07, 0.47], p = 0.145; Std. beta = 0.20, 95% CI [-0.07,
## 0.47])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald z-distribution approximation.## The model included Belief as random effects (formula: list(~1 + Belief + Avatar | SubjectID, ~1 + Belief | TrialID))## boundary (singular) fit: see help('isSingular')## [1] "very strong evidence against"
## (Rules: jeffreys1961)## [1] 0.01563404## [1] 0.01563404## boundary (singular) fit: see help('isSingular')## [1] "very strong evidence against"
## (Rules: jeffreys1961)## [1] 0.02970183## [1] 0.02970183## boundary (singular) fit: see help('isSingular')## [1] "no evidence against or in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUEInitiator Total Overt Attention
Plot
Load Data and Identify Factors
##### Linear Mixed Effects Models
Load Data and Identify Factors
| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | 926.484 | 104.169 | 68.282 | 8.894 | 0.000 |
| BeliefHuman | 125.535 | 135.263 | 64.529 | 0.928 | 0.357 |
| AvatarRobot | 74.183 | 86.726 | 62.269 | 0.855 | 0.396 |
| BeliefHuman:AvatarRobot | -97.580 | 109.600 | 56.466 | -0.890 | 0.377 |
## (Intercept) BeliefHuman AvatarRobot
## 926.48382 125.53531 74.18283
## BeliefHuman:AvatarRobot
## -97.57970
## boundary (singular) fit: see help('isSingular')
| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | 8.087 | 0.112 | 31.367 | 71.906 | 0.00 |
| BeliefHuman | 0.090 | 0.150 | 61.244 | 0.602 | 0.55 |
| AvatarRobot | -0.019 | 0.065 | 51.599 | -0.294 | 0.77 |
## (Intercept) BeliefHuman AvatarRobot
## 8.08702120 0.09007677 -0.01921343## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: TOAT ~ Belief + Avatar + (1 + Belief + Avatar | SubjectID) +
## (1 + Belief | TrialID)
## Data: iTotalOAData
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
##
## REML criterion at convergence: 11693.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.1385 -0.5624 0.0448 0.5502 4.1781
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## TrialID (Intercept) 0.01475 0.1214
## BeliefHuman 0.01398 0.1182 -1.00
## SubjectID (Intercept) 0.32876 0.5734
## BeliefHuman 0.40210 0.6341 -0.47
## AvatarRobot 0.16736 0.4091 -0.42 0.20
## Residual 1.01494 1.0074
## Number of obs: 4002, groups: TrialID, 72; SubjectID, 65
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 8.08702 0.11247 31.36742 71.906 <2e-16 ***
## BeliefHuman 0.09008 0.14970 61.24401 0.602 0.55
## AvatarRobot -0.01921 0.06540 51.59866 -0.294 0.77
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlfHmn
## BeliefHuman -0.698
## AvatarRobot -0.336 0.095
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')## boundary (singular) fit: see help('isSingular')## Random effect variances not available. Returned R2 does not account for random effects.## boundary (singular) fit: see help('isSingular')## Random effect variances not available. Returned R2 does not account for random effects.## We fitted a linear mixed model (estimated using REML and BOBYQA optimizer) to
## predict TOAT with Belief and Avatar (formula: TOAT ~ Belief + Avatar). The
## model included Belief as random effects (formula: list(~1 + Belief + Avatar |
## SubjectID, ~1 + Belief | TrialID)). The model's explanatory power related to
## the fixed effects alone (marginal R2) is 1.95e-03. The model's intercept,
## corresponding to Belief = AI and Avatar = Anthropomorphic, is at 8.09 (95% CI
## [7.87, 8.31], t(3989) = 71.91, p < .001). Within this model:
##
## - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.09, 95% CI [-0.20, 0.38], t(3989) = 0.60, p = 0.547; Std. beta =
## 0.08, 95% CI [-0.17, 0.33])
## - The effect of Avatar [Robot] is statistically non-significant and negative
## (beta = -0.02, 95% CI [-0.15, 0.11], t(3989) = -0.29, p = 0.769; Std. beta =
## -0.02, 95% CI [-0.13, 0.09])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.## The model included Belief as random effects (formula: list(~1 + Belief + Avatar | SubjectID, ~1 + Belief | TrialID))## boundary (singular) fit: see help('isSingular')## [1] "extreme evidence against"
## (Rules: jeffreys1961)## [1] 7.804832e-07## [1] 7.804832e-07## boundary (singular) fit: see help('isSingular')## [1] "extreme evidence against"
## (Rules: jeffreys1961)## [1] 7.804832e-07## [1] 7.804832e-07## boundary (singular) fit: see help('isSingular')## [1] "extreme evidence against"
## (Rules: jeffreys1961)## [1] 6.573804e-09## [1] 6.573804e-09## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUEInitiator Overt Attention Before Partner Response
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Load Data and Identify Factors
##### Linear Mixed Effects Models
Load Data and Identify Factors
| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | 819.066 | 102.218 | 69.309 | 8.013 | 0.000 |
| BeliefHuman | 116.751 | 131.098 | 64.494 | 0.891 | 0.376 |
| AvatarRobot | 54.845 | 90.275 | 61.712 | 0.608 | 0.546 |
| BeliefHuman:AvatarRobot | -126.744 | 112.689 | 55.783 | -1.125 | 0.266 |
## (Intercept) BeliefHuman AvatarRobot
## 819.06647 116.75052 54.84452
## BeliefHuman:AvatarRobot
## -126.74361
| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | 5.937 | 0.080 | 66.185 | 74.286 | 0.000 |
| BeliefHuman | 0.111 | 0.103 | 61.687 | 1.076 | 0.286 |
| AvatarRobot | 0.007 | 0.070 | 61.394 | 0.096 | 0.924 |
| BeliefHuman:AvatarRobot | -0.112 | 0.088 | 55.718 | -1.272 | 0.209 |
## (Intercept) BeliefHuman AvatarRobot
## 5.936890746 0.110827056 0.006739816
## BeliefHuman:AvatarRobot
## -0.111642861## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: iOABRT ~ Belief + Avatar + Belief:Avatar + (1 + Avatar | SubjectID) +
## (1 | TrialID)
## Data: iOABRespData
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
##
## REML criterion at convergence: 7163
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7039 -0.5870 0.0357 0.5729 4.0256
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## TrialID (Intercept) 0.003524 0.05936
## SubjectID (Intercept) 0.135700 0.36838
## AvatarRobot 0.064180 0.25334 -0.20
## Residual 0.408067 0.63880
## Number of obs: 3550, groups: TrialID, 72; SubjectID, 65
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 5.93689 0.07992 66.18480 74.286 <2e-16 ***
## BeliefHuman 0.11083 0.10296 61.68711 1.076 0.286
## AvatarRobot 0.00674 0.07007 61.39397 0.096 0.924
## BeliefHuman:AvatarRobot -0.11164 0.08775 55.71765 -1.272 0.209
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlfHmn AvtrRb
## BeliefHuman -0.770
## AvatarRobot -0.375 0.291
## BlfHmn:AvtR 0.299 -0.348 -0.799## We fitted a linear mixed model (estimated using REML and BOBYQA optimizer) to
## predict iOABRT with Belief and Avatar (formula: iOABRT ~ Belief + Avatar +
## Belief:Avatar). The model included Avatar as random effects (formula: list(~1 +
## Avatar | SubjectID, ~1 | TrialID)). The model's total explanatory power is
## substantial (conditional R2 = 0.28) and the part related to the fixed effects
## alone (marginal R2) is of 4.27e-03. The model's intercept, corresponding to
## Belief = AI and Avatar = Anthropomorphic, is at 5.94 (95% CI [5.78, 6.09],
## t(3541) = 74.29, p < .001). Within this model:
##
## - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.11, 95% CI [-0.09, 0.31], t(3541) = 1.08, p = 0.282; Std. beta =
## 0.15, 95% CI [-0.12, 0.42])
## - The effect of Avatar [Robot] is statistically non-significant and positive
## (beta = 6.74e-03, 95% CI [-0.13, 0.14], t(3541) = 0.10, p = 0.923; Std. beta =
## 9.03e-03, 95% CI [-0.17, 0.19])
## - The effect of Belief [Human] × Avatar [Robot] is statistically
## non-significant and negative (beta = -0.11, 95% CI [-0.28, 0.06], t(3541) =
## -1.27, p = 0.203; Std. beta = -0.15, 95% CI [-0.38, 0.08])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.## The model included Avatar as random effects (formula: list(~1 + Avatar | SubjectID, ~1 | TrialID))## [1] "anecdotal evidence in favour of"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "anecdotal evidence against"
## (Rules: jeffreys1961)## [1] 1## [1] 1## [1] "extreme evidence against"
## (Rules: jeffreys1961)## [1] 0.008235511## [1] 0.008235511## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUEInitiator Overt Attention After Partner Response
Plot
Load Data and Identify Factors
Linear Mixed Effects Models
Load Data and Identify Factors
| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | 297.819 | 8.666 | 109.348 | 34.365 | 0.000 |
| BeliefHuman | 0.994 | 6.266 | 49.792 | 0.159 | 0.875 |
| AvatarRobot | 60.035 | 7.635 | 69.127 | 7.863 | 0.000 |
| BeliefHuman:AvatarRobot | 6.829 | 9.746 | 63.893 | 0.701 | 0.486 |
## (Intercept) BeliefHuman AvatarRobot
## 297.8194411 0.9939506 60.0352097
## BeliefHuman:AvatarRobot
## 6.8287011
| Estimate | Std. Error | df | t value | Pr(>|t|) | |
|---|---|---|---|---|---|
| (Intercept) | 13.056 | 0.119 | 115.046 | 110.105 | 0.000 |
| BeliefHuman | 0.012 | 0.099 | 50.144 | 0.124 | 0.902 |
| AvatarRobot | 0.762 | 0.100 | 64.121 | 7.605 | 0.000 |
| BeliefHuman:AvatarRobot | 0.102 | 0.127 | 58.668 | 0.805 | 0.424 |
## (Intercept) BeliefHuman AvatarRobot
## 13.05551772 0.01223464 0.76245916
## BeliefHuman:AvatarRobot
## 0.10238862## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## ResponseT ~ Belief + Avatar + Belief:Avatar + (1 + Avatar | SubjectID) +
## (1 | TrialID)
## Data: iOAResponseData
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 50000))
##
## REML criterion at convergence: 9617.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.9511 -0.2891 0.1889 0.5297 4.0254
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## TrialID (Intercept) 0.58079 0.7621
## SubjectID (Intercept) 0.06941 0.2635
## AvatarRobot 0.08716 0.2952 0.59
## Residual 1.38139 1.1753
## Number of obs: 2939, groups: TrialID, 72; SubjectID, 65
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 13.05552 0.11857 115.04587 110.105 < 2e-16 ***
## BeliefHuman 0.01223 0.09871 50.14393 0.124 0.902
## AvatarRobot 0.76246 0.10025 64.12123 7.605 1.58e-10 ***
## BeliefHuman:AvatarRobot 0.10239 0.12712 58.66794 0.805 0.424
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) BlfHmn AvtrRb
## BeliefHuman -0.511
## AvatarRobot -0.121 0.146
## BlfHmn:AvtR 0.095 -0.137 -0.789## We fitted a linear mixed model (estimated using REML and BOBYQA optimizer) to
## predict ResponseT with Belief and Avatar (formula: ResponseT ~ Belief + Avatar
## + Belief:Avatar). The model included Avatar as random effects (formula: list(~1
## + Avatar | SubjectID, ~1 | TrialID)). The model's total explanatory power is
## substantial (conditional R2 = 0.40) and the part related to the fixed effects
## alone (marginal R2) is of 0.07. The model's intercept, corresponding to Belief
## = AI and Avatar = Anthropomorphic, is at 13.06 (95% CI [12.82, 13.29], t(2930)
## = 110.10, p < .001). Within this model:
##
## - The effect of Belief [Human] is statistically non-significant and positive
## (beta = 0.01, 95% CI [-0.18, 0.21], t(2930) = 0.12, p = 0.901; Std. beta =
## 8.06e-03, 95% CI [-0.12, 0.14])
## - The effect of Avatar [Robot] is statistically significant and positive (beta
## = 0.76, 95% CI [0.57, 0.96], t(2930) = 7.61, p < .001; Std. beta = 0.50, 95% CI
## [0.37, 0.63])
## - The effect of Belief [Human] × Avatar [Robot] is statistically
## non-significant and positive (beta = 0.10, 95% CI [-0.15, 0.35], t(2930) =
## 0.81, p = 0.421; Std. beta = 0.07, 95% CI [-0.10, 0.23])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.## The model included Avatar as random effects (formula: list(~1 + Avatar | SubjectID, ~1 | TrialID))## [1] "extreme evidence against"
## (Rules: jeffreys1961)## [1] 0## [1] 0## [1] "extreme evidence against"
## (Rules: jeffreys1961)## [1] 0## [1] 0## [1] "extreme evidence against"
## (Rules: jeffreys1961)## [1] 0## [1] 0## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUE## [1] TRUEANOVA for Total Overt Attention
## Bin width defaults to 1/30 of the range of the data. Pick better value with
## `binwidth`.
## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?
## Bin width defaults to 1/30 of the range of the data. Pick better value with
## `binwidth`.
## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?## Df Sum Sq Mean Sq F value Pr(>F)
## Belief 1 64430 64430 0.321 0.573
## Residuals 63 12662393 200990##
## Shapiro-Wilk normality test
##
## data: aov_residuals
## W = 0.87774, p-value = 1.115e-05##
## Kruskal-Wallis rank sum test
##
## data: MeanTotalOA by Belief
## Kruskal-Wallis chi-squared = 0.38768, df = 1, p-value = 0.5335## [1] TRUE## [1] TRUEOvert Attention Summary
Frequency of Initiator Overt Attention
## [1] TRUE## [1] TRUEInitiator Total Overt Attention
## [1] TRUE## [1] TRUEInitiator Overt Attention Before Partner Response
## [1] TRUE## [1] TRUEInitiator Overt Attention After Partner Response
## [1] TRUE## [1] TRUE